Are you having to argue a specific side of a debate? Your question is one-sided, as Post 3 points out; so you need to first determine whether Canada does provide better health care. The best way to do this is to read evaluations from citizens of both country who have been provided with health care in each country. Their firsthand experience would be difficult to argue with.
Also, consider whether more Canadians travel to the States seeking American health services or whether more Americans travel to Canada seeking health care there.
The assumption in the question is that Canada actually provides better healthcare than the US. Certainly everyone in Canada is covered through the government; if the assumption is that government provided healthcare is better because everyone's covered, then by definition Canada provides better healthcare. The fundamental issue in the healthcare question is how to provide the best medical services for the most people at the cheapest cost, and the answer lies beyond politics. To implement a system that would respect each of those three variables is simply beyond the power of any government; what government should do is allow for systematic changes to occur so each of those variables can be maximized.
It's pretty hard to prove that one country or the other has better health care. That's because it's pretty hard to define what better health care is.
Candians live 2 or 3 years longer on average than Americans. It turns out that a lot of that is because we have more murders in the US. Much of the rest of the gap is because Americans have more heart attacks. Now it's hard to tell if that is because of them having better health care or if it's because more than 30% of Americans are obese while the Canadian rate is 17% for men and 19% for women. So it's hard to prove they do have better health care.
As far as how their system works, they have a single-payer system where the government provides health insurance to everyone. The government does not actually provide the health care, unlike in Britain, for example. Instead, the government provides the insurance and the individual finds a doctor.
Other than that, I'm not sure what you're asking. Are you asking about the mechanics of the system or are you asking why their system can work even though it's not like ours?